The difficulties of synthesis of pure Aurivillius phases largely impede them from extensive application. In this work, the first principles thermodynamics approach was applied to investigate the phase competition relation of three homologous Aurivillius series C Bi2Nb2O9-n NaNbO3, Bi4Ti3O12-n SrTiO3 and Bi4Ti3O12-n CaTiO3, in order to uncover the thermodynamic mechanism of the phase stability. The competition among different phases was analyzed by the relative Gibbs energy as a function of chemical potentia...